President Trump has used Twitter to threaten “Little Rocket Man,” but he and Kim Jong Un have since developed a “beautiful” relationship through a more old-fashioned means of communication: paper letters.

The president, who typically eschews diplomatic protocols, has warmed to the “historic” and “groundbreaking” mash notes from the North Korean dictator, who has been accused of committing human rights atrocities. At a Cabinet meeting this week, Trump waved a new one and declared that people he’s shown it to have “never written letters like that.”

To Trump, the handful of letters he’s received from Kim since their June summit in Singapore offer an easy retort to reports that his high-stakes bid to persuade the regime to surrender its nuclear weapons program has stalled.

Though direct talks have gone cold since North Korean negotiators canceled a meeting with Secretary of State Mike Pompeo in early November, the written communiques have remained warm and injected a sense of comity in the talks, aides said, offering Trump a reason to continue.

The letters are usually passed between American and North Korean diplomats who meet at the demilitarized zone of the Korean Peninsula, said an official familiar with the procedure. Among those who have accepted letters for Trump are Harry Harris, the U.S. ambassador to South Korea, and his deputy, the official said.

Trump is so smitten that he privately shows off the notes to guests in the Oval Office, summoning an aide to bring in two stacks of papers — one set in Korean and another translated into English, according to those who have seen them.

The letters contain flowery praise, employing honorifics such as “Your Excellency,” which Kim used in a July 6 note that Trump released publicly. Kim touted Trump’s “energetic and extraordinary efforts” and lauded the “epochal progress” of the bilateral relationship.

Former U.S. diplomats scoffed at the idea that Kim’s letters are a sign of increasing personal trust and meaningful progress. Rather, they suggested, Kim has sized up his mark and showered the president with flattery to soften him up at the negotiating table.

“The letters are illustrative of the way that Trump operates and perceives things — that it’s all about him,” said Daniel Russel, who served as a high-level Asia policy official in President Barack Obama’s administration.

Russel noted that in his televised annual New Year’s Day address, Kim reiterated demands that the United States agree to remove its nuclear umbrella in defense of South Korea before Pyongyang takes commensurate steps.

Once eager to convince Trump of his willingness to denuclearize, Kim has now reverted more openly to the North’s longtime strategy without feeling “a need to tiptoe around it,” Russel said. “He’s determined that his customer is very anxious to make a deal and that he, Kim Jong Un, can now start setting the terms with greater clarity.”

Past presidents have written letters to communicate with isolated regimes with which Washington does not have regular diplomatic contact. Obama, for example, sent secret letters in 2014 to the supreme leader of Iran, Ayatollah Ali Khamenei, when his administration was negotiating a nuclear deal with Tehran.

Former U.S. officials said the letters aim to build trust, but they acknowledged that they have limited effects. In 2007, with the United States slogging through the fourth year of “six-party talks” with North Korea, Assistant Secretary of State Christopher Hill, the chief U.S. negotiator, asked his boss, Condoleezza Rice, if President George W. Bush would write a note to then-dictator Kim Jong Il, the current leader’s father, who died in 2011.

Bush said no, Hill recalled in an interview, so he moved to Plan B and persuaded the president to write a letter to the leaders of the other nations using nearly identical language. Hill passed the note to a North Korean official on a trip to Pyongyang in December 2007, but Kim Jong Il never responded.

Still, Hill is skeptical that Kim Jong Un’s letters demonstrate tangible progress. “That’s complete nonsense,” he said. If anything, Hill added, the messages have further eroded the diplomatic isolation that was once part of Trump’s “maximum pressure” campaign on Pyongyang.

Others have taken a more benign view of the letters.

“A good personal rapport between leaders can certainly help negotiators find ways to overcome obstacles in difficult talks between longtime adversaries, but in the end what matters are the decisions and actions approved by those leaders,” said Daryl Kimball, executive director of the Arms Control Association.

Obama also reached out to Kim Jong Il through a letter in 2009, his first year in office. The one-page note, on White House letterhead, echoed Obama’s public statements, said Russel, who helped deliver it in Pyongyang.

The president urged Kim to “honor a strong commitment to denuclearization” and emphasized that the United States had “no hostile intent” and was open to a “fresh start,” Russel said. But once again, Kim Jong Il did not reply.

For the younger Kim, who has sought to boost his country’s economic fortunes by persuading foreign nations to lift crippling sanctions, the letters have provided a strategic opening to bypass lower-level U.S. officials and directly woo Trump, who during his 2016 campaign questioned the costs of keeping U.S. troops in South Korea and Japan.

In late May, just two weeks before his summit with Kim, Trump abruptly called it off in a tart letter in which he chided the North Korean leader for the “tremendous anger and open hostility” toward the United States. Trump warned that the U.S. nuclear capabilities “are so massive and powerful that I pray to God they will never have to be used.”

Trump aides point to that moment as a breakthrough. Kim dispatched Pyongyang’s top negotiator, Kim Yong Chol, to visit the White House, where he presented to Trump a symbolic oversize envelope with a note signed by his boss. They posed for a photo with it in the Oval Office.

“That letter was a very nice letter,” Trump told reporters, before admitting that he had not yet read it. “I may be in for a big surprise, folks,” he said.

In fact, Trump has only grown more affectionate for his North Korean counterpart, boasting at a campaign rally in West Virginia in September that “we fell in love” after exchanging letters. Later that month, at the U.N. General Assembly in New York, Trump called one note from Kim “a beautiful piece of art.”

The White House confirmed that Trump responded to at least one of the letters Kim has sent since their summit in Singapore, but that response has not been publicly released.

Trump’s aides reject criticism of his approach, emphasizing that he has kept tough economic sanctions in place. As for the president, he has reaffirmed his willingness to meet again with Kim this year, while bemoaning a lack of credit for his efforts.

“It’s been this way for 80 years,” he said of the hostility with North Korea, which was founded in 1948. “If another administration came in . . . you’d be having a nice big, fat war in Asia.”